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Quantum Information and Measurement (QIM)

Optical Back-action Evading Measurement of Mechanical Oscillator

Liu Qiu, Itay Shomroni, Daniel Malz, Andreas Nunnenkamp, Tobias Jan Kippenberg

Published Jan 1, 2019• 1 citation
Publisher

Abstract

Quantum mechanics sets a limit on continuous position measurement of a harmonic oscillator, due to quantum backaction from quantum fluctuations in the measurement field. We demonstrate continuous optical two-tone backaction-evading measurement of a mechanical mode of a photonic crystal nanobeam.
DOI
10.1364/qim.2019.s1c.2

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When measuring the position of a mechanical oscillator, quantum mechanics imposes a strict limit on the attainable precision: Any reduction of imprecision leads to increased quantum backaction of the measuring probe on the oscillator. This quantum limit can be circumvented, in principle allowing to indefinitely reduce imprecision, by monitoring only a single quadrature of the oscillator. Such backaction-evading measurement has been recently demonstrated in electromechanical oscillators coupled to microwave resonant circuits. Here we demonstrate this technique in a photonic crystal nanomechanical oscillator, cryogenically and optomechanically cooled to a few quanta.
The standard quantum limit constrains the precision of an oscillator position measurement. It arises from a balance between the imprecision and the quantum backaction of the measurement. However, a measurement of only a single quadrature of the oscillator can evade the backaction and be made with arbitrary precision. Here we demonstrate quantum backaction evading measurements of a collective quadrature of two mechanical oscillators, both coupled to a common microwave cavity. The work allows for quantum state tomography of two mechanical oscillators, and provides a foundation for macroscopic mechanical entanglement and force sensing beyond conventional quantum limits.
We propose here a fully backaction-evading scheme for the measurement of the entanglement between two nanomechanical resonators. The system, which consists of two mechanical oscillators, coupled to a single mode of an electromagnetic resonant cavity through a radiation-pressure interaction term, is driven by two pump tones and four detection tones. As previously discussed in the literature, the former induce entanglement between the two mechanical oscillators, while we show here that a specific choice of phase and amplitude of the detection tones allows for direct pairwise reconstruction of the collective quadrature fluctuations of the mechanical oscillators belonging to quantum-mechanics-free subspaces, thereby providing direct evidence of the entanglement properties of the two mechanical resonators.
Backaction-evading measurements of mechanical motion can achieve precision below the zero-point uncertainty and quantum squeezing, which makes them a resource for quantum metrology and quantum information processing. We provide an exact expression for the conditional state of an optomechanical system in a two-tone backaction-evading measurement beyond the standard adiabatic approximation and perform extensive numerical simulations to go beyond the usual rotating-wave approximation. We predict the simultaneous presence of conditional mechanical squeezing, intracavity squeezing, and optomechanical entanglement. We further apply an analogous analysis to the multimode optomechanical system of two mechanical and one cavity mode and find conditional mechanical Einstein-Podolski-Rosen entanglement and genuinely tripartite optomechanical entanglement. Our analysis is of direct relevance for ultrasensitive measurements and measurement-based control in high-cooperativity optomechanical sensors operating beyond the adiabatic limit.
We present the exact analytical solution of the explicitly time-periodic quantum Langevin equation describing the dual-beam backaction-evading measurement of a single mechanical oscillator quadrature due to V. B. Braginsky, Y. I. Vorontsov, and K. S. Thorne [Science 209, 547 (1980)] beyond the commonly used rotating-wave approximation. We show that counterrotating terms lead to extra sidebands in the optical and mechanical spectra and to a modification of the main peak. Physically, the backaction of the measurement is due to periodic coupling of the mechanical resonator to a light-field quadrature that only contains cavity-filtered shot noise. Since this fact is independent of other degrees of freedom the resonator might be coupled to, our solution can be generalized, including to dissipatively or parametrically squeezed oscillators, as well as recent two-mode backaction-evading measurements.